The main predictor is early childhood reading for pleasure. A suspicion is that the early start gives a lead that is almost impossible to make up, as life gets more busy, not less, when people get older.

Early childhood pleasure reading requires parents that have enough reading skill themselves and the free time to teach you how to read, and childhood access to a wide variety of interesting books at a range of levels. Those are things that are going to be correlated with your parents' wealth. And your grandparents' wealth. As a slave descendant, my parents were the first people in the history of my family who were able to read easily. One still had to pick cotton as a child to get spending money.